Suppose that $5 \%$ of men and $0.25 \%$ of women have grey hair. $A$ person with grey hair is selected at random. What is the probability of this person being male? Assume that there are equal numbers of males and females.

An examination is attempted by $5000$ graduates, $2000$ post-graduates, and $1000$ doctorate holders. The probabilities that a graduate, a post-graduate, and a doctorate holder will pass the examination are $\frac{2}{3}$, $\frac{3}{4}$, and $\frac{4}{5}$ respectively. If one of the examinees passed the examination, then the probability that he is a post-graduate is:

In an entrance test,there are multiple-choice questions. There are four possible answers to each question,of which one is correct. The probability that a student knows the answer to a question is $9/10$. If he gets the correct answer to a question,then the probability that he was guessing is:

There are three bags $X$,$Y$,and $Z$. Bag $X$ contains $5$ one-rupee coins and $4$ five-rupee coins; Bag $Y$ contains $4$ one-rupee coins and $5$ five-rupee coins; and Bag $Z$ contains $3$ one-rupee coins and $6$ five-rupee coins. $A$ bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability that it came from bag $Y$ is:

In four schools $B_1, B_2, B_3, B_4$,the percentage of girl students is $12, 20, 13, 17$ respectively. From a school selected at random,one student is picked up at random and it is found that the student is a girl. The probability that the school selected is $B_2$ is:

$A$ diagnostic test has a probability of $0.95$ of giving a positive result when applied to a person suffering from a certain disease and a probability of $0.10$ of giving a positive result when given to a non-sufferer. It is estimated that $0.5 \%$ of the population are suffering from the disease. If this test is administered to a person from this population about whom there is no information relating to the incidence of this disease and the test gives a positive result, then the probability that the person is a sufferer is: